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Simplifying 2(t + -2) + -3(2t + -3) = 5 + -5(3t + 2) Reorder the terms: 2(-2 + t) + -3(2t + -3) = 5 + -5(3t + 2) (-2 * 2 + t * 2) + -3(2t + -3) = 5 + -5(3t + 2) (-4 + 2t) + -3(2t + -3) = 5 + -5(3t + 2) Reorder the terms: -4 + 2t + -3(-3 + 2t) = 5 + -5(3t + 2) -4 + 2t + (-3 * -3 + 2t * -3) = 5 + -5(3t + 2) -4 + 2t + (9 + -6t) = 5 + -5(3t + 2) Reorder the terms: -4 + 9 + 2t + -6t = 5 + -5(3t + 2) Combine like terms: -4 + 9 = 5 5 + 2t + -6t = 5 + -5(3t + 2) Combine like terms: 2t + -6t = -4t 5 + -4t = 5 + -5(3t + 2) Reorder the terms: 5 + -4t = 5 + -5(2 + 3t) 5 + -4t = 5 + (2 * -5 + 3t * -5) 5 + -4t = 5 + (-10 + -15t) Combine like terms: 5 + -10 = -5 5 + -4t = -5 + -15t Solving 5 + -4t = -5 + -15t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15t' to each side of the equation. 5 + -4t + 15t = -5 + -15t + 15t Combine like terms: -4t + 15t = 11t 5 + 11t = -5 + -15t + 15t Combine like terms: -15t + 15t = 0 5 + 11t = -5 + 0 5 + 11t = -5 Add '-5' to each side of the equation. 5 + -5 + 11t = -5 + -5 Combine like terms: 5 + -5 = 0 0 + 11t = -5 + -5 11t = -5 + -5 Combine like terms: -5 + -5 = -10 11t = -10 Divide each side by '11'. t = -0.9090909091 Simplifying t = -0.9090909091
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